code: def test_sylvester():
      x = var("x")
  
      assert (
          sylvester(x**3 - 7, 0, x)
          == sylvester(x**3 - 7, 0, x, 1)
          == Matrix([[0]])
      )
      assert (
          sylvester(0, x**3 - 7, x)
          == sylvester(0, x**3 - 7, x, 1)
          == Matrix([[0]])
      )
      assert sylvester(x**3 - 7, 0, x, 2) == Matrix([[0]])
      assert sylvester(0, x**3 - 7, x, 2) == Matrix([[0]])
  
      assert (
          sylvester(x**3 - 7, 7, x).det()
          == sylvester(x**3 - 7, 7, x, 1).det()
          == 343
      )
      assert (
          sylvester(7, x**3 - 7, x).det()
          == sylvester(7, x**3 - 7, x, 1).det()
          == 343
      )
      assert sylvester(x**3 - 7, 7, x, 2).det() == -343
      assert sylvester(7, x**3 - 7, x, 2).det() == 343
  
      assert (
          sylvester(3, 7, x).det()
          == sylvester(3, 7, x, 1).det()
          == sylvester(3, 7, x, 2).det()
          == 1
      )
  
      assert (
          sylvester(3, 0, x).det()
          == sylvester(3, 0, x, 1).det()
          == sylvester(3, 0, x, 2).det()
          == 1
      )
  
      assert (
          sylvester(x - 3, x - 8, x)
          == sylvester(x - 3, x - 8, x, 1)
          == sylvester(x - 3, x - 8, x, 2)
          == Matrix([[1, -3], [1, -8]])
      )
  
      assert (
          sylvester(x**3 - 7 * x + 7, 3 * x**2 - 7, x)
          == sylvester(x**3 - 7 * x + 7, 3 * x**2 - 7, x, 1)
          == Matrix(
              [
                  [1, 0, -7, 7, 0],
                  [0, 1, 0, -7, 7],
                  [3, 0, -7, 0, 0],
                  [0, 3, 0, -7, 0],
                  [0, 0, 3, 0, -7],
              ]
          )
      )
  
      assert sylvester(
          x**3 - 7 * x + 7, 3 * x**2 - 7, x, 2
      ) == Matrix(
          [
              [1, 0, -7, 7, 0, 0],
              [0, 3, 0, -7, 0, 0],
              [0, 1, 0, -7, 7, 0],
              [0, 0, 3, 0, -7, 0],
              [0, 0, 1, 0, -7, 7],
              [0, 0, 0, 3, 0, -7],
          ]
      )
  
imports: from sympy.core.symbol import var
  from sympy.polys.polytools import pquo, prem, sturm, subresultants
  from sympy.matrices import Matrix
  from sympy.polys.subresultants_qq_zz import sylvester, res, res_q, res_z, bezout, subresultants_sylv, modified_subresultants_sylv, subresultants_bezout, modified_subresultants_bezout, backward_eye, sturm_pg, sturm_q, sturm_amv, euclid_pg, euclid_q, euclid_amv, modified_subresultants_pg, subresultants_pg, subresultants_amv_q, quo_z, rem_z, subresultants_amv, modified_subresultants_amv, subresultants_rem, subresultants_vv, subresultants_vv_2
label_desc: Use image node_id 1 for calling a global function with example usage: test_sylvester() without return types